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## Feedback control systems characteristics Solutions-chapter 4

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**1. **Feedback control systems characteristics Solutions-chapter 4
Prof. Marian S. Stachowicz
Laboratory for Intelligent Systems
ECE Department, University of Minnesota Duluth
February 23, 2010

**2. **References for reading
R.C. Dorf and R.H. Bishop, Modern Control Systems,
11th Edition, Prentice Hall, 2008,
Chapter 4.1 - 4.11
2. J.J. DiStefano, A. R. Stubberud, I. J. Williams, Feeedback and Control Systems, Schaum's Outline Series, McGraw-Hill, Inc., 1990
Chapter 9 2 Control Systems

**3. **Outline Introduction
Error signal analysis
Sensitivity of control systems to parameter variations
Disturbance signals in a feedback control system 3 Control Systems Objectives
The main topic of Chapters 2 and 3 was the mathematical modeling of physical systems. In this chapter we extend the ideas of modeling to include control system characteristics, such as sensitivity to model uncertainties, steady-state errors, transient response characteristics to input test signals, and disturbance rejection. We investigate the important role of the system error signal. This signal is used to control the process using the notion of feedback. Generally speaking, the goal is to minimize the error signal.
We will also develop the concept of the sensitivity of a system to a parameter change, since it is desirable to minimize the effects of unwanted parameter variation. We then describe the transient performance of a feedback system and show how this performance can be readily improved.
We wish to reduce the effect of unwanted input signals, called disturbances, on the output signal. We will show how we may design a control system to reduce the impact of disturbance signals. Of course, the benefits of a control system come with an attendant cost. We will demonstrate how the cost of using feedback in a control system is associated with the selection of the feedback sensor device. The chapter concludes with a system performance analysis of the Sequential Design Example: Disk Drive Read System.
Objectives
The main topic of Chapters 2 and 3 was the mathematical modeling of physical systems. In this chapter we extend the ideas of modeling to include control system characteristics, such as sensitivity to model uncertainties, steady-state errors, transient response characteristics to input test signals, and disturbance rejection. We investigate the important role of the system error signal. This signal is used to control the process using the notion of feedback. Generally speaking, the goal is to minimize the error signal.
We will also develop the concept of the sensitivity of a system to a parameter change, since it is desirable to minimize the effects of unwanted parameter variation. We then describe the transient performance of a feedback system and show how this performance can be readily improved.
We wish to reduce the effect of unwanted input signals, called disturbances, on the output signal. We will show how we may design a control system to reduce the impact of disturbance signals. Of course, the benefits of a control system come with an attendant cost. We will demonstrate how the cost of using feedback in a control system is associated with the selection of the feedback sensor device. The chapter concludes with a system performance analysis of the Sequential Design Example: Disk Drive Read System.

**4. **Goal We extend the ideas of modeling to include control system characteristics:
- sensitivity to model uncertainties,
- steady-state errors,
- transient response characteristics to input test signals,
- disturbance rejection. Control Systems 4

**5. **Feedback control 5 Control Systems Negative feedbackNegative feedback

**6. **6 Control Systems Figure: 04-01Figure: 04-01

**7. **Advantages of the closed-loop feedback control Decreased sensitivity of the system to variations in the parameters of the process
Improved rejection of the disturbances
Improved measurement noise attenuation
Improved reduction of the steady-state error of the system
Easy control and adjustment of the transient response 7 Control Systems

**8. **System sensitivity 8 Control Systems

**9. **System sensitivity 9 Control Systems

**10. **10 Control Systems it confirms that the T changes by the same percentage as the process gain.it confirms that the T changes by the same percentage as the process gain.

**11. **11 Control Systems Figure: 04-02Figure: 04-02

**12. **12 Control Systems

**13. **The sensitivity of the feedback system to change in the G(s) 13 Control Systems

**14. **The sensitivity of the feedback system to change in the H(s) 14 Control Systems

**15. **15 Control Systems Figure: 04-03abFigure: 04-03ab

**16. **Closed-loop control system 16 Control Systems

**17. **Closed-loop control system 17 Control Systems

**18. **18 Control Systems

**19. **19 Control Systems

**20. **20 Control Systems Tracking the sun to obtain maximum power from a photovoltaic array.
May be represented by Fig. 4.3 with H(s) = 1 and G(s)= 100/(? s + 1), where ? = 3 sec. Tracking the sun to obtain maximum power from a photovoltaic array.
May be represented by Fig. 4.3 with H(s) = 1 and G(s)= 100/(? s + 1), where ? = 3 sec.

**21. **Sensitivity 21 Control Systems

**22. **Time-constant 22 Control Systems for Laplace Table (? s + 1) = ? (s +1/?)for Laplace Table (? s + 1) = ? (s +1/?)

**23. **Step responses 23 Control Systems

**24. **24 Control Systems Compute : T(s), Tracking error E(s) = R(s) - Y(s), Steady state tracking error due to a unit step input, R(s) = 1/s,
Transfer function Y(s)/Td(s) of the output due to a unit step disturbance input Td(s) =1/s
Sensitivity T(s,K)Compute : T(s), Tracking error E(s) = R(s) - Y(s), Steady state tracking error due to a unit step input, R(s) = 1/s,
Transfer function Y(s)/Td(s) of the output due to a unit step disturbance input Td(s) =1/s
Sensitivity T(s,K)

**25. **The transfer function 25 Control Systems

**26. **Tracking error 26 Control Systems

**27. **The steady-state error 27 Control Systems

**28. **Sensitivity 28 Control Systems

**29. **29 Control Systems Is to be controlled so that it closes to an angle ? by using a DC motor system.
Determine: the response ?(t) to a step change in ?d(t) when K = 20
Find the effect of a load disturbance Td(s0 = A/s
Determine the steady state err or essr when the input is r(t) t, t>0 ( assume that Td(s) = 0)Is to be controlled so that it closes to an angle ? by using a DC motor system.
Determine: the response ?(t) to a step change in ?d(t) when K = 20
Find the effect of a load disturbance Td(s0 = A/s
Determine the steady state err or essr when the input is r(t) t, t>0 ( assume that Td(s) = 0)

**30. **ECE 3151 Figure: 04-16 The DLR German Aerospace Center is developing an advanced robotic hand. The hand operator receives stereo video feedback and force feedback. This information is employed in conjunction with a data glove equipped with force feedback and an input devise to control robotFigure: 04-16 The DLR German Aerospace Center is developing an advanced robotic hand. The hand operator receives stereo video feedback and force feedback. This information is employed in conjunction with a data glove equipped with force feedback and an input devise to control robot

**31. **Control Systems 31

**32. **Transfer function 32 Control Systems

**33. **Disturbance 33 Control Systems

**34. **Final value 34 Control Systems

**35. **AP 4.3 The machine tool 35 Control Systems A machine tool is designed to follow a desired path so that r(t) = (1 - t) u(t)
Determine:
The steady-state error when r(t) is the desired path and Td(s)=0
Plot the error e(t) for r(t) for 0< t <10 sec
Find the steady -state error when Td(s) = 1/s and r(t) = 0
Plot the error e(t) for previous partA machine tool is designed to follow a desired path so that r(t) = (1 - t) u(t)
Determine:
The steady-state error when r(t) is the desired path and Td(s)=0
Plot the error e(t) for r(t) for 0< t <10 sec
Find the steady -state error when Td(s) = 1/s and r(t) = 0
Plot the error e(t) for previous part

**36. **Error plot 36 Control Systems

**37. **37 Control Systems

**38. **38 Control Systems

**39. **39 Control Systems Figure: 04-38-34UNAP4.6Figure: 04-38-34UNAP4.6

**40. **40 Control Systems

**41. **41 Control Systems

**42. **42 Control Systems

**43. **43 Control Systems

**44. **CP 4.3 Family of step responses 44 Control Systems

**45. **45 Control Systems To regulate the level h in response to a disturbance change q3.To regulate the level h in response to a disturbance change q3.

**46. **46 Control Systems

**47. **47 Control Systems

**48. **48 Control Systems The temperature T of the process is controlled by the heater with resistance RThe temperature T of the process is controlled by the heater with resistance R

**49. **Open-loop response of the system 49 Control Systems It is not a transfer function. Rather it is a Y(s).
The linearized open-loop response of the system.
Determine and compare the open-loop and closed-loop system for
Sensitivity to changes to constant K=k1kaEb
b) The ability to to reduce the effects of a step disturbance in the environmental temperature ?Te(s)
c) The steady state error of the temperature controller for a step change in the input e-desired.
It is not a transfer function. Rather it is a Y(s).
The linearized open-loop response of the system.
Determine and compare the open-loop and closed-loop system for
Sensitivity to changes to constant K=k1kaEb
b) The ability to to reduce the effects of a step disturbance in the environmental temperature ?Te(s)
c) The steady state error of the temperature controller for a step change in the input e-desired.

**50. **50 Control Systems

**51. **51 Control Systems

**52. **52 Control Systems

**53. **53 Control Systems